Leaving the whole string uncut might be not so dangerous, but looks really messy and "hippie".
Cutting the extra string away guarantees that some day it will puncture your finger tip.

I do not like too much of "Jacksons or Floyd Roses", but stringing them is clever. Because You can not get the string end (with the ball) through the bridge hole, I've stringed it through the tuning axel. The ball stays there on the headstock and on the bridge I just cut away the extra and stick the string end in to the bridge - no worries there!

But on a "normal" guitar - how do You do with the string ends? Leave it messy, or dangerous - or something else?

Of course there's the ideal fender shaft too where You can "hide" the string end inside the tuning pole, but that's something I don't have on every guitar..

Haha I stick to Fenders with the vintage style split shafts so I never have the ends giving me trouble!
I do have a few without the split and just cut the ends as short as possible to avoid punctures.
There's always locking tuners to hide the ends, and I'm looking for a set of aluminum Sperzels for a LP with Grovers on it.

All of my Fenders have split shaft vintage and surprise surprise, my first real guitar, an Ibanez Artist Series semi-hollowbody came with hybrid tuners that are split and also have a hole like regular tuners. I use them as split shaft and have no worries.

Vintage split shaft tuners here so no problems, on my grover tuner guitars I cut the string as close as possible to the post. I do the z bend thing so no troublesome knots to hamper the string ends being close to the shaft.

On sub-normal guitars that insist on displaying hypodermic weaponry, I snip to around 3-5mm after stretching out and tuning to pitch, then bend the offending stabulata at 90 degrees downwards. This ensures the fluffy case liners and my delicate fingers remain unviolated.

I spin the ends into a little pigtail around the peghead(doubling back opposite direction to lock it in place), then cut it with an inch or so of curl. This gives it some suspension and movement so if it pokes me it won't go straight in like a hypodermic needle!

Those cut strings ends can rip the heck out of the inside of a gig bag too.
I cut the ends with enough room left to bend them in towards the headstock with needle nose pliers; like this. (usually a little shorter than pictured)
Don't let them touch the headstock itself and scratch it.
S Mac

I use the knot method of securing the strings, minimal wraps and then use diagonal flush cutters to cut as tight to the mess as possible. I have one pair of cutters that are used for only this purpose. They sit in my guitar maintenance toolbox. This has worked for me for a good number of years now.

Why have those dangerous pokers,, how about none? I got this tip from Steve Kimock.

Lots of wraps
Wrap a few winds on the high side of the pegs string/hole, then the rest of the wraps go underneath the string/hole. Break the string by tight circular movements at the base where excess string meet the hole.

No pokers and excellent grip, if done correctly there's no need to tighten up any slack or 'stretch', just tune and go on stage.